99-31
On the generation of discrete isotropic orientation distributions for linear elastic crystals
by Bertram, A.; Böhlke, T.; Gaffke, N.; Heiligers, B.; Offinger, R.
Preprint series: 99-31, Preprints
- MSC:
- 62K99 None of the above but in this section
- 62N99 None of the above but in this section
- 15A90 Applications of matrix theory to physics
Abstract: We consider a model for the elastic behaviour of a polycrystalline material based of volume averages. In this case the effective elastic properties depend only on the distribution of the orientations over the grains. The aggregate is assumed to consist of a finite number of grains each of which behaves elastically like a cubic single crystal. The material parameters are fixed over the grains. An important problem is to find discrete orientation distributions (DODs) which are isotropic, i.e., whose VOIGT and REUSS averages of the grain stiffness tensors coincide with those one would obtain under a continous and homogeneous distribution of orientations. We succeed in finding isotropic DODs for any even number of grains $N \geq 4$ and uniform volume fractions of the grains. Also, $N = 4$ is shown to be the minimum number of grains for an isotropic DOD.
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